There has been known a solid oxide fuel cell (SOFC) which acts at a comparatively high temperature wherein an anode gas is supplied to one side and a cathode gas (air, etc.) is supplied to the other side. The fuel cell system using a fuel cell like this needs a time before it is completely stopped because this fuel cell must be cooled (JP 2007-066876A). For example, among stationary fuel cell systems, there are some which require one to several days before they are completely stopped.